math16B-sp06-mt2-Sarason-exam-1

math16B-sp06-mt2-Sarason-exam-1 - 8832832888 18:58...

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Unformatted text preview: 8832832888 18:58 5188422418 LICE MflIN LIERflR‘r" F'flGE 81.385 Mathematics 16B April 5, 2006 Sarason MIDTERM EXAMINATION 2 Name (Printed): Signature: 1 2 3.1—, . SID Number: El Torn Dorsey El Zak Mesyan TOTAL GET (check one): D David Penneys Gfifivfig CI Arun Shanna PO Section Number or Time: Put your name on every page. Closed book except for crib sheet. No calculators. SHOW YOUR WORK. Cross out anything you have written that you do not wish the grader to consider. Make sure the grader can easily spot your final answer(s] to each question, for example by boxing the answers. The points for each problem are in parentheses. Perfect score t 70. 8832832888 18:58 5188422418 LICE Mn’l‘qIN LIERflR‘r" 888E 82.385 Name 2 1. (20) Perform the integrations. ‘1'? 71' (a) I] =/ ISiIl(1‘2)dI (b) 12 = / $231113: :13: [I . D 8832832888 18:58 5188422418 LICE Mn’l‘qIN LIERflR‘r" 888E 88.385 N ame ‘ 3 2. (20) For the clifierential equation 1;“ = ——(y + 1)2(t + 1]: (a) What are the constant solutions1 if any? (b) What is the general solution? (C) What is the solution satisfying the initial condition MO) = D? 8832832888 18:58 5188422418 LICE Mn’l‘qIN LIERflR‘r" 888E 84.385 Name 4 3. (20) Roger Rover invests $300,000 in a real estate trust, which will pay annual interest of 6%, compounded continuously. He arranges for $1,000 per month to he transferred from his account in the trust to his ex-wife Grouchita‘s bank account, in payment of alimony. (a) Assuming the transfers to Grouchita’s account are made continuously, set up a differential equation satisfied by the balance P(t) in Roger’s trust account at time t {where t is measured in years, with t = 0 corresponding to the inception of the account) _ (b) Find the general solution of the diflerential equation. (c) Find the particular solution describing Roger’s account. (d) Find an expression for the time it will take for Roger‘s account to grow to $400000. 8832832888 18:58 5188422418 LICE Mn’l‘qIN LIERflR‘r" 888E 85.385 Name 4. (10) An airliner in. the fleet of Krate Airways flies at a constant speed of 10 miles / minute along a straight path at a constant altitude of 5 miles. At noon, the plane is directly above radar station A, which records the angle of elevation 9(13) of the plane as seen from A, as a function of time. Assuming t is measured in minutes with t fl 0 corresponding to noon, find 6’(1] in. radians/minute. ...
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